Elastic response of surface-loaded half plane with influence of surface and couple stresses

Le, Toan Minh; Lawongkerd, Jintara; Bui, Tinh Quoc; Limkatanyu, Suchart; Rungamornrat, Jaroon

doi:10.1016/j.apm.2020.09.034

Cited by 15 publications

(5 citation statements)

References 69 publications

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“…The Somigliana identities in couple stress theory can then be derived by using the reciprocal theorem (20) assuming that one of the equilibrium solutions coincides with the fundamental solution. Moreover, in what follows we also assume that the body forces and body couples vanish in the actual state, i.e.…”

Section: Boundary Integral Formulationmentioning

confidence: 99%

See 1 more Smart Citation

An Isogeometric Boundary Element Formulation for Stress Concentration Problems in Couple Stress Elasticity

Hattori

Trevelyan

Gourgiotis

2022

Preprint

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Section: Boundary Integral Formulationmentioning

confidence: 99%

“…[4][5][6][7]). The couple stress theory has been successfully employed recently to model microstructured materials and pertinent size effects in various areas such as fracture [8][9][10][11], contact [12][13][14][15][16][17], stress/strain localization [18][19][20][21], and wave propagation problems [22,23].…”

Section: Introductionmentioning

confidence: 99%

An Isogeometric Boundary Element Formulation for Stress Concentration Problems in Couple Stress Elasticity

Hattori

Trevelyan

Gourgiotis

2022

Preprint

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“…This model has been utilized in the study of elastic domains with coupled surface and internal stresses, for example, in problems involving tangential line loading (e.g. [Le et al, 2021]).…”

Section: Analysis Of Fractures In Nano-structures Accounting For Surf...mentioning

confidence: 99%

Energy Release Rate, the crack closure integral and admissible singular fields in Fracture Mechanics

Piccolroaz,

Peck,

Wrobel

et al. 2021

Preprint

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One of the assumptions of Linear Elastic Fracture Mechanics is that the crack faces are tractionfree or, at most, loaded by bounded tractions. The standard Irwin's crack closure integral, widely used for the computation of the Energy Release Rate, also relies upon this assumption. However, there are practical situations where the load acting on the crack boundaries is singular. This is the case, for instance, in hydraulic fracturing, where the fluid inside the crack exerts singular tangential tractions at its front. Another example of unbounded tractions is the case of a rigid line inclusion (anticrack) embedded into an elastic body. In such situations, the classical Irwin's crack closure integral fails to provide the correct value of the Energy Release Rate. In this paper, we address the effects occurring when square-root singular tractions act at the boundary of a line defect in an elastic solid and provide a generalisation of Irwin's crack closure integral. The latter yields the correct Energy Release Rate and allows broad applications, including, among others, hydraulic fracturing, soft materials containing stiff inclusions, rigid inclusions, shear bands and cracks characterized by the Gurtin-Murdoch surface stress elasticity. We present the results in the most general form, where six Stress Intensity Factors are present: three of them are classical SIFs corresponding to the modes I-II-III and computed under the assumption of homogeneous boundary conditions at the defect surfaces, while the other three SIFs are associated with singular admissible tractions (those that lead to a finite ERR value). It is demonstrated that this approach resolves an ambiguity in using the same SIF's terminology in the cases of open cracks and rigid inclusions, among other benefits.

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“…The response of a surface-loaded half plane under the influence of surface and couple stresses has been observed by Zhou and Li (2019). Le et al (2021) studied the Yoffe-type moving crack in piezoelectric quasicrystals. An et al (2022) investigated the dynamic stress intensity factor (DSIF) at the crack tip of magnetic-electro-elastic biomaterials with mode-III interface fracture.…”

Section: Introductionmentioning

confidence: 99%

On the dynamic mode-III crack in the elastic continuum consisting of sandy properties

Yadav,

Renu

2023

Phys. Scr.

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The aim of the present investigation is to come up with a mathematical model for the dynamic mode III crack in an elastic continuum consisting of sandy properties. For the analysis of the propagating mode-III crack due to the propagating Love-type wave in an elastic continuum consisting of sandy properties, the results for the stress intensity factor (SIF) and crack opening displacement (COD) have been developed in closed form. The complex variable integral transform mathematical methods consisting of the two-sided Fourier integral transform, along with the Weiner-Hopf technique, serve as a salient feature of the adopted mathematical treatment for determining the SIF and COD in the closed form. Moreover, the expressions for the SIF and COD for the limiting static mode-III crack have also been obtained and deduced for special cases of elastic medium. The effects of existing parameters, viz. dry sandiness parameter, depth of crack, crack velocity on the SIF and COD . The effect of physical materials parameters has been shown numerically as well as graphically.

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Elastic response of surface-loaded half plane with influence of surface and couple stresses

Cited by 15 publications

References 69 publications

An Isogeometric Boundary Element Formulation for Stress Concentration Problems in Couple Stress Elasticity

An Isogeometric Boundary Element Formulation for Stress Concentration Problems in Couple Stress Elasticity

Energy Release Rate, the crack closure integral and admissible singular fields in Fracture Mechanics

On the dynamic mode-III crack in the elastic continuum consisting of sandy properties

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